CAT Practice : Mensuration

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This is one of the questions which looks difficult on first look but with a little visualization and concept, can be cracked in a minute. This kind of question is more likely to appear in CAT.

Spheres and Cubes

    Q.10: A spherical shaped sweet is placed inside a cube of side 5 cm such that the sweet just fits the cube. A fly is sitting on one of the vertices of the cube. What is the shortest distance the fly must travel to reach the sweet?
    1. 2.5 cm
    2. 5(√3 – 1) cm
    3. 5(√2 – 1) cm
    4. 2.5(√3 – 1) cm


  • Correct Answer
    Choice D. 2.5(√3 – 1) cm

Detailed Solution

Diagram :

The question demands visualization. The shortest distance required to be travelled by the fly would be diagonally and be given by:-

Distance =

= (Since diagonal of the cube is given as √3 x l)


= 2.5(√3 – 1)

Choice (D) is therefore, the correct answer.

Correct Answer: 2.5(√3 – 1) cm

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More questions from Mensuration

  1. Cone and Frustum
  2. Spheres
  3. Circles and Chords
Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.